BOSTON -- Beaches in South Boston and East Boston were significantly cleaner in 2013 than in past years, while improper sewage hookups and other pollutants continue to contaminate the water at Lynn, Swampscott, Dorchester and Quincy swimming spots, according to Save the Harbor Save the Bay’s third annual report card.

“The biggest story remains South Boston,” said Save the Harbor director of communications and programs Bruce Berman. He said, “Those beaches used to be closed one out of every five days not so very long ago.”

Beaches in South Boston and East Boston had bacteria levels below the state swimming standard nearly 100 percent of the time based on daily testing in 2013. Malibu Beach in a basin near Savin Hill, and Tenean Beach at a Dorchester inlet met that mark 76 and 63 percent of the time, respectively.

Wollaston Beach in Quincy passed the standard 88 percent of the time, according to Save the Harbor. Nantasket Beach in Hull, the only other South Shore beach included in the report, received a perfect score.

Berman said efforts in East Boston to ferret out old, illegal hookups that sent sewage into storm drains “really made a difference.” Constitution Beach in East Boston passed the bacteria standard 88 percent of the time in 2012 and 97 percent of the time in 2013, when there was much more rain and therefore greater risk of sewage or other pollutants washing into the harbor.

The House and Senate this year have passed bills aimed at financing better water infrastructure, and encouraging new techniques for handling sewage with grants. Berman said he wants the Senate to include $20 million in funding for improvements to Metro Boston beaches the House added to an environmental bond bill, and said the money would be spent cleaning up the waters around Dorchester, Quincy, Lynn and Swampscott.

“Tenean and King’s are consistently the worst,” said Berman, who said Tenean is also storm-damaged and “needs to be remade.”

High levels of bacteria can lead to upset stomach, diarrhea and ear infections and eye infections, Berman said.

Last year the state began requiring two days of tests exceeding state standards before a red flag would be flown to indicate a beach closure, Berman said. He said the tests take 24 hours to complete and under the previous system where a single test could trigger a closure, the water was often clean by the time a beach was closed.

Berman said the beaches with vastly improved water quality can now have their monitoring reduced to weekly tests, and said, “It’s time to fix the other ones.”

Berman said Tenean likely suffers for its proximity to the Neponset River’s mouth and commercial dog walkers who use a nearby park.